PSI - Issue 7

Yoichi Yamashita et al. / Procedia Structural Integrity 7 (2017) 11–18 Yoichi Yamashita et Al./ Structural Integrity Procedia 00 (2017) 000–000

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Garwood, M.F., Zurburg, H.H., and Erickson, M.A., 1951. Correlation of Laboratory Tests and Service Performance, Interpretation of Tests and Correlation with Service, ASM, Philadelphia, PA, pp. 1–77. Masuo, H., Tanaka, Y., Morokoshi, S., Yagura, H., Uchida, T. Yamamoto, Y. Murakami, Y., 2017, Effects of Defects, Surface Roughness and HIP on Fatigue Strength of Ti-6Al-4V manufactured by Additive Manufacturing, Structural Integrity/Procedia, 3 rd Int. Sym. FDMD, Lecco, Italy. Murakami, Y. and Endo, M., 1994. Effects of defects, inclusions and inhomogeneities on fatigue strength, Int. J. Fatigue, Vol.16, pp.163-182. Murakami, Y., Beretta, S., 1999. Small defects and inhomogeneities in fatigue strength: experiment, models and statistical implications, Extremes, 2(2), 123-147. Murakami, Y. and Nemat-Nasser, S. 1983. Growth and Stability of Interacting Surface Flaws of Arbitrary Shape, Engng. Frac. Mech., 17-1, 193-210. Nishijima, S., 1980. Statistical Analysis of Fatigue Test Data, J. Soc. Mater. Sci., Japan, 29(316) , 24–29. Appendix Brief Summary of the √ area Parameter Model Many fatigue limit prediction models have been proposed. Regarding the material parameters, most of models adopt one or more fatigue data such as ∆ K th or ∆ J R or S - N data. If we adopt the reference fatigue data which were obtained in a condition close to a prediction problem, the model may be accurate. However, such a model is a kind of so-called data fitting model and cannot be easily applied to other materials. In the √ area parameter model, only one material parameter, Vickers hardness HV , is used. The reason is that there is the robust empirical relationship between HV and σ w for HV <400 as follows (Fig. 3). σ w = 1.6 HV ± 0.1 HV (A1) Where, the units are σ w in MPa and HV in kgf/mm 2 . Based on FEM analysis, the background of Eq. (A1) can be correlated to tensile strength and cyclic stress-strain constitutive property. For HV >400, fatigue limit cannot attain the value of Eq. (A1) and drops due to presence of small defects and nonmetallic inclusions. It is known that if there exists defects larger than a critical size, the value of Eq. (A1) cannot be guaranteed even for HV <400. Therefore, we need to seek the geometrical parameter which crucially reflects the fatigue threshold. Based on the concept, the square root of the projection area of defects, √ area , was discovered as the representative geometrical parameter which expresses the maximum stress intensity factor K max along the front of 3D crack as shown in Fig. A1. Thus, using one material parameter, HV , and one geometrical parameter, √ area , and examining many fatigue data on artificial small defects, the prediction equation for small cracks and defects was developed as follows. σ w = C 0 ( HV +120)/( √ area ) 1/6 (A2) Where, C 0 = 1.43 for surface cracks and C 0 = 1.56 for subsurface cracks, and the units are σ w : MPa, HV : kgf/mm 2 , √ area : µ m. In Eq. (A2), the term ( HV + 120) must be carefully interpreted, because σ w is not simply proportional to HV . For example, the quantity ( HV + 120) is doubled for HV = 120. But it is only 1.2 HV for HV = 600. Adding a constant 120 to HV reflects the easiness of crack closure for soft metals. Thus, the √ area parameter model is not a simple empirical formula but it was made based on the thorough consideration on the fracture mechanics and a strength parameter which includes the intrinsic strength of microstructure and crack closure tendency. Equation (A2) is not valid for a very small defect if the value of σ w calculated by Eq. (A2) exceeds the fatigue limit of unnotched specimen σ w0 . Such a very small defect must be regarded as non-damaging defect. On the other hand, for valid application of Eq. (A2) there is the upper bound of √ area depending on HV of materials. Murakami, Y., 2002. Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, Elsevier. Murakami, Y., 2012. Material defects as the basis of fatigue design, Int. J. Fatigue, Vol.41, pp.2-10 .

Fig. A1